Question

The area of a minor sector of a circle is 3.85 cm² and the measure of its central angle is 36^°. Find the radius of the circle.

Answer 1

Area of minor sector of the circle = 3.85 cm²
The measure of a central angle, θ = 36º
Let the radius of the circle be r cm.
Now,
Area of minor sector = 3.85 cm² 

\[\Rightarrow \frac{\theta}{360° } \times \pi r^2 = 3 . 85\]

\[ \Rightarrow \frac{36° }{360 ° } \times \frac{22}{7} \times r^2 = 3 . 85\]

\[ \Rightarrow r = \sqrt{\frac{3 . 85 \times 360°  \times 7}{36°  \times 22}}\]

\[ \Rightarrow r = \sqrt{12 . 25} = 3 . 5 cm\]

Thus, the radius of the circle is 3.5 cm .